Stats 3y03 midterm 1 practice PDF

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Midterm 1 STATS 3Y03 MCMASTERProblem #1: Events A , B , C are independent with P [ A ] = 0, P [ B ] = 0, P[ C ] = 0. The probability P [ A B C ] is:(A) 0 (B) 0 (C) None of these (D) 0. Problem #1: A Correct Answer: AYour Mark: 1/1 Problem #2: You get on an elevator at the ground floor with two other...

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Midterm 1 STATS 3Y03 MCMASTER Problem #1: Events A, B, C are independent with P[A]  =  0.2, P[B]  =  0.3, P[C]  =  0.4. The probability P[A   B   C] is: (A) 0.6640 (B) 0.9000 (C) None of these (D) 0.9760 Correct Answer: A Problem #1: A

Your Mark: 1/1

Problem #2: You get on an elevator at the ground floor with two other people. The

elevator is going up and there are five floors above ground. Each of the three persons selects a floor to exit at random. The probability that everyone gets off at a different floor is: (A) 0.375 (B) 0.960 (C) 0.480 (D) 0.125 Correct Answer: C Problem #2: C

Your Mark: 1/1 Problem #3: In a city, 60% of households use a local cable company for internet, 50% use that company for television, and 30% use that company for both internet and cable. The percent of households that use that

company for exactly one of the services (internet or cable but not both) is: (A) 10% (B) 30% (C) 20% (D) 50% Correct Answer: D Problem #3: D

Your Mark: 1/1

Problem #4: The table below gives information on the percentage of people purchasing a cup of coffee at a shop based on size and type of coffee. regular decaffeinated

small

medium

large

10% 15%

25% 20%

20% 10%

If a customer is selected at random, the probability that she selects a large decaffeinated coffee is: (A) 0.10 (B) 0.45 (C) 0.30 (D) None of these Correct Answer: A Problem #4: D

Your Mark: 0/1

Problem #5: In question 4 if a customer is randomly selected, the conditional probability that she selects a large coffee given that she selected a decaffeinated is:

(A) 0.22 (B) 0.30 (C) 0.45 (D) 0.33 Correct Answer: A Problem #5: A

Your Mark: 1/1

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Problem #6: If four fair coins are tossed, the probability mass function of X, the number of heads obtained, is given by: x f  ( x)

0

1

2

3

4

0.0625

0.2500

0.3750

0.2500

0.0625

The probability of getting more heads than tails is: (A) 0.2500 (B) 0.3125 (C) 0.5000 (D) 0.0625 Correct Answer: B Problem #6: B

Your Mark: 1/1

Problem #7: A bin contains 50 items of which 10% are defective. Five items are selected at random without replacement. Let X denote the number of defectives in the sample of five. The probability P[X  =  3] is: (A) 0.0050 (B) 0.0033 (C) 0.0047 (D) 0.0030 Correct Answer: C Problem #7: B

Your Mark: 0/1

Problem #8: Suppose that the random variable X has the following probability mass function. x  f( x)

0 0.1

1 0.4

2 0.3

3 0.2

The mean E[X] is: (A) 2.0 (B) 1.6 (C) 1.0 (D) 1.5 Correct Answer: B Problem #8: B

Your Mark: 1/1

Problem #9: Referring to Problem 8, the variance V[X] is: (A) 0.84 (B) 1.25 (C) 0.61 (D) 0.95 Correct Answer: A Problem #9: A

Your Mark: 1/1

Problem #10: The table below gives the probability mass function of sales of flash drives Y at a computer store where Y is the size of the drive in GB. y   f( y)

1 0.05

16 0.10

32 0.35

64 0.40

128 0.10

The cumulative distribution F(64) is: (A) 0.50 (B) 0.40 (C) 0.75 (D) 0.90 Correct Answer: D Problem #10: C

Your Mark: 0/1

Problem #11: The diagram below shows the probabilities that the individual switches operate (that is, are closed). The switches act independently. Find the probability that there is a path of closed switches across the circuit from left to right.

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(A) 0.9865 (B) 0.9950 (C) 0.9375 (D) 0.9995 Correct Answer: A Problem #11: A

Your Mark: 1/1

Problem #12: The proportion of voters who support a change in government in a population of 20 million is 0.4. Let X be the number of voters in a random sample of 1000 voters who support a change in government. The mean and standard deviation of X are, respectively, (A) 400 and 0.0155 (B) 0.4 and 0.76 (C) 400 and 12.62 (D) 400 and 15.49 Correct Answer: D Problem #12: C

Your Mark: 0/1 Problem #13: A roofing contractor offers an inexpensive method of fixing leaky roofs. However, the job is not foolproof since he estimates that 15% of the roofs will still leak. If the contractor is hired to fix 12 roofs, what is the probability that at most 1 will still leak after the repairs.

(A) 0.34 (B) 0.82 (C) 0.44 (D) 0.20 Correct Answer: C Problem #13: C

Your Mark: 1/1

Problem #14: Pulses arrive at a counter according to a Poisson distribution having an average λ = 2 pulses per minute. Let X denote the number of pulses arriving during a 5 minute interval. P[9  ≤  X  ≤  11] is: (A) 0.2388 (B) 0.5000 (C) 0.3640 (D) 0.4766 Correct Answer: C Problem #14: A

Your Mark: 0/1

Problem #15: Let X be a continuous random variable with probability density function 6x(1 − x) 0  ...